REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE

doi:10.1016/S0252-9602(16)30009-1

Abstract

Abstract:

We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)∇u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and without any restriction on the upper growth p of nonlinearity, except that p>2, we show the existences of random attractor in D₀^{1, 2}(D_{N, σ})∩ L^?(D_N)(?∈[2, 2p-2]) space, where D_N is an arbitrary (bounded or unbounded) domain in R^N, N≥2. For this purpose, some abstract results based on the omega-limit compactness are established.

Key words: Random dynamical systems, stochastic degenerate parabolic equation, multiplicative noise, random attractors, Wiener process

CLC Number:

35B40

Wenqiang ZHAO. REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE[J].Acta mathematica scientia,Series B, 2016, 36(2): 409-427.

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